Question

A solid sphere of radius $r$ is revolving about one of its diameters with an angular velocity $\omega$. If it suddenly expands uniformly so that its radius increases to $n$ times its original value, then its angular velocity becomes

• A. $n^2 \omega$
• B. $\frac{\omega}{n^2}$
• C. $n \omega$
• D. $\frac{\omega}{n}$
• E. $2 n \omega$

Answer 1

Answer: (B)

$I_{1} \omega_{1}=I_{2} \omega_{2}$
$\frac{2}{5} m r^{2} \omega=\frac{2}{5} m\left(r'\right)^{2} \times \omega_{2}$
$r^{2} \omega=(n r)^{2} \omega_{2}$
$r^{2} \omega=n^{2} r^{2} \omega_{2}$
$\omega_{2}=\frac{\omega}{n^{2}}$